You'll quite often see two reports from a single command, one for TCP and one for UDP. The PID and user is shown for each IP socket, so if you see something suspicious, you can investigate further (e.g., with ps -l 5763 to get more information on the mysql process here, or by looking at /proc/5763/).

For a real-time look at what's being opened where, try watch lsof -i (hit Ctrl-C to exit). To check out who's connecting to your web server, specify the port with lsof -i :80: You'll get a list that shows which IP addresses or hosts are looking at your web server right now. You can also check connections to a particular host with lsof -i@hostname.example.com (or give the IP address instead).

You can get similar information on which Unix sockets are open on your machine, with lsof -U. Unix sockets handle inter-process communication, a bit like IP sockets but within a single machine rather than across a network. This information can be useful when using strace to track down bugs.